The Galerki Approach for Finite Elements of Field Functions: The Case of Buckling in GRP
- 1 Department of Industrial ? Production Engineering, Nnamdi Azikiwe University Awka, Nigeria
Abstract
This paper used the equation of the deflected axis of a beam to present procedures for solving one-dimensional functions that can be expressed in the form of Poisson equation. The equation of the deflected axis of a beam was solved for deflection for GRP composite component by Finite Element Method (FEM) using integrated FEM-Galerki approach to derive the finite elements equations. The critical stress of GRP structure at the onset of structural instability was computed as 14.162 MPa using Euler relation while the maximum bending moment, a subject in the equation of the deflected axis of a beam of structure was also estimated with classical relation. The equation of the deflected axis of the beam is then solved as a one dimensional Poisson equation following FEM-Galerki approach for deriving element equation. The maximum optimum deflection a measure of maximum instability occurring around the mid span of element of structure was estimated. Also the finite element predicted results were compared with analytical results and the finite element results captured the general trend of the analytical results.
- Hawkes, B. and Abinett, R., (1985). The Engineering Design Process, Pitman Publishing.p101.
- Ihueze, C.C., (2005).Optimum Buckling Response Model of GRP Composites, Ph.D Thesis, University of Nigeria. p111.
- Chapra, S.C and Canale, R.P., (1998). Numerical Methods for Engineers, McGraw-Hill Publishers, 3 rd edition, Boston, N.Y. p853.
- Astley, R.J., (1992). Finite Elements in Solids and Structures, Chapman and Hall Publishers, UK. p154.
- Enetanya, A.N. and Ihueze, C. C., (2008). Computational Approaches for Strengths of GRP Composites. Journal of Engineering and Applied Sciences, vol.4 No.1 and 2. P62.
- Black, P.H. and Adams, O.E., (1981).Machine Design. McGraw-Hill International Book Company, Tokyo. p41.
- Benham, P.P. and Warnock, F.V., (1981). Mechanics of Solids and Structures. Pitman Books, Toronto. p257.
- Beer, F. P. and Johnston, B., (1977). Vector Mechanics for Engineers (Statics), 3 rd edition. McGraw-Hill Book Company, New York. p354.
- Koshal, D., (1998). Manufacturing Engineers Reference Book, Butterworth Heinemann Publisher. p102.
- Rosen, B.W., (1965). Mechanics of Composite Strengthening: Fibre Composite Materials, American Society of Metals, Chapter 3.
- Kyriakides, S., Perry, E.J., and Liechti, K.M., (1994). Instability and failure of fibre composites in compressive, ASME Journal of Applied Mechanics, Vol. 47, No. 6, S 262– 266.
- Zienkiewicz, O.C., (1977). The Finite Element Method: Basic Formulation and Linear Problems, 3 rd ed., vol.1, McGraw-Hill, London. p228-301.